Limited-thread enumeration for non-inner-connected graphs

Determine whether walks of non-inner-connected directed graphs can be enumerated with a limited number of threads, analogously to the approach for deterministic automata.

Background

Inner-connectedness characterizes the existence of bounded push-pop walk orderings, but the paper also discusses enumeration algorithms with constrained resources. For non-inner-connected graphs, bounded one-thread orderings are impossible, yet it remains unresolved whether enumeration can nevertheless be performed using a limited number of threads, as in prior work on automata.

References

Another question is whether walk enumeration on non-inner-connected graphs can be done with a limited number of threads like in; we expect that our results would generalize but leave this open.

— Graphs with Bounded Push-Pop Walk Orderings  (2610.19724 - Amarilli et al., 14 Oct 2026) in Section “Conclusion and Future Directions”